Rybakina, ranked 10th in the world after a runner-up finish to Aryna Sabalenka at the Australian Open in January, had lost her last three matches against Badosa.

She said a solid service game and the upper hand on a few key points allowed her to turn the tables on Badosa – her doubles partner in the California desert.

She fired nine aces and benefitted from seven double faults by Badosa, converting four of her break point chances against the Spaniard while dropping her own serve just once.

“I try to focus on the points,” said the Kazakhstan player, who kept her cool after falling down a break in the second set. “Especially when it’s tough, I try to change a bit the serve. It’s not easy, sometimes also you start thinking about yourself, emotions.

“It’s not easy always to actually act on these important moments.”

Rybakina said the slow Indian Wells courts coupled with some gusty winds made for difficult conditions.

“Today the ball was flying much more,” she said. “But I’m trying to adapt. For now it was successful.”

Men’s defending champion Taylor Fritz said the winds required a different approach from each side of the net, but the Californian adapted admirably in a 6-1, 6-2 victory over Argentina’s Sebastian Baez.

“The wind is definitely tough to deal with,” said Fritz, the fourth seed. “On one side you have to hit the ball a lot harder to just get it over the net.

“And then on the other side it’s a little tougher to go big because it’s pretty easy to send it long.”

The two matches were part of a Stadium Court programme that featured top seeds Carlos Alcaraz and Iga Swiatek battling to reach the round of 16 in the combined WTA and ATP Masters 1000 event.

Spain’s Alcaraz, who can return to number one in the world with a third Masters 1000 triumph, faced Tallon Griekspoor of the Netherlands while women’s number one Swiatek – winner of the French and US Opens last year and the defending Indian Wells champion – faced Canadian Bianca Andreescu.

Swiatek is seeking to become just the second woman, after Martina Navratilova in 1990-91, to win back-to-back Indian Wells titles.

Andreescu won Indian Wells in 2019, springboard to a breakout season that included a US Open crown.

• Garcia outlasts Fernandez -

In other early matches, women’s fifth seed Caroline Garcia advanced with 6-4, 6-7 (5/7), 6-1 victory over Canadian Leylah Fernandez, a rematch of an Australian Open second-round clash won by the French player.

Garcia’s early aggressiveness paid off with the lone break of the opening set. After Fernandez, the 2021 US Open runner-up, grabbed the second set tiebreaker Garcia steadied herself to pull away in the third.

Garcia saved two break points on her opening service game, and then she was off and running.

“I tried to stay with more intensity and fighting,” Garcia said. “That’s what I did better in the third set, I fought better and I put more pressure.”

Former US Open champion Emma Raducanu also reached the round of 16, downing Brazilian Beatriz Haddad Maia 6-1, 2-6, 6-4.

Three-time Grand Slam champion Stan Wawrinka scored a win for the old guard, beating 19-year-old seventh seed Holger Rune 6-2, 6-7 (5/7), 7-5.

A former world number three now ranked 100th as he bids to return from injury, 37-year-old Wawrinka had 18 years on his opponent, but he avenged a first-round defeat to the Dane at the Paris Masters in November, where Rune saved three match points to launch his run to a first Masters title. Former world number one Andy Murray, 35 and trying to grind his way back after hip replacement surgery in 2019, was also in action, taking on 21-year-old British compatriot Jack Draper.